At $25^{\circ}C$,$20.0 \ mL$ of $0.2 \ M$ weak monoprotic acid $HX$ is titrated against $0.2 \ M$ $NaOH$. The $pH$ of the solution $(a)$ at the start of the titration (when $NaOH$ has not been added) and $(b)$ when $10 \ mL$ of $NaOH$ is added respectively,are:
Given: $K_a = 5 \times 10^{-4}, pK_a = 3.3, \alpha << 1$

The ionization constant of dimethylamine is $5.4 \times 10^{-4}$. Calculate its degree of ionization in its $0.02 \ M$ solution. What percentage of dimethylamine is ionized if the solution is also $0.1 \ M$ in $NaOH$?

Conductivity of $0.00241 \, M$ acetic acid is $7.896 \times 10^{-5} \, S \, cm^{-1}$. Calculate its molar conductivity. If $\Lambda_m^o$ for acetic acid is $390.5 \, S \, cm^2 \, mol^{-1}$,what is its dissociation constant?

When $100 \ mL$ of $1.0 \ M \ HCl$ was mixed with $100 \ mL$ of $1.0 \ M \ NaOH$ in an insulated beaker at constant pressure,a temperature increase of $5.7^{\circ} C$ was measured for the beaker and its contents (Expt. $1$). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $\left(-57.0 \ kJ \ mol ^{-1}\right)$,this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. $2$),$100 \ mL$ of $2.0 \ M$ acetic acid $\left(K_a=2.0 \times 10^{-5}\right)$ was mixed with $100 \ mL$ of $1.0 \ M \ NaOH$ (under identical conditions to Expt. $1$) where a temperature rise of $5.6^{\circ} C$ was measured.
(Consider heat capacity of all solutions as $4.2 \ J \ g ^{-1} K ^{-1}$ and density of all solutions as $1.0 \ g \ mL ^{-1}$)
$1.$ Enthalpy of dissociation (in $kJ \ mol ^{-1}$) of acetic acid obtained from the Expt. $2$ is
$(A) \ 1.0 \ (B) \ 10.0 \ (C) \ 24.5 \ (D) \ 51.4$
$2.$ The $pH$ of the solution after Expt. $2$ is
$(A) \ 2.8 \ (B) \ 4.7 \ (C) \ 5.0 \ (D) \ 7.0$
Give the answer for question $1$ and $2.$

In which of the following equations will $\alpha_1$ or $\alpha_2$ be higher?
$(i) \, NH_4OH + H_2O \rightarrow \alpha_1$
$(ii) \, NH_4OH + D_2O \rightarrow \alpha_2$

$30 \ cc$ of $\frac{M}{3} \ HCl$,$20 \ cc$ of $\frac{M}{2} \ HNO_{3}$ and $40 \ cc$ of $\frac{M}{4} \ NaOH$ solutions are mixed and the volume was made up to $1 \ dm^{3}$. The $pH$ of the resulting solution is